There are many chess variants, and most are crap. There's actually just ONE variant I thoroughly enjoy (see below why). It is called shrink-chess . If you like chess, check it out, it is truly fun.
The Rules.
(1) When a row or colum becomes empty, it dissapears from play.
Of course, there are four rows empty in the beginning. But, the rule says becomes empty. I.e. it has to be non-empty, and then becomes empty. For example, if you play
1. Ng1-f3
and after that play 1. Nf3-d4
then the third row disappears from play, and the knight is standing in front of its pawns (at "d3"). This is the only real rule change. You do this on the board by moving all pieces above row 3 one row down. (Or the pieces below row 3 up.) You can have things like that you cannot move a piece, as it would shrink, and you'd be in chess. For example, put white: Ka1, Na3, Ba2 and black: Nb4 as in the below diagram:
Then you cannot move the bishop, as the second row would disappear, and the black knight would attack the king. Hence, the bishop is fixed.
You can have strange mates this way. For example, put white Kc1, black pawns at a3,b2,d2, e3, b3 as in the below diagram
then white is mate.
Obviously, you can end up with two bishops of the same color, etc.
Anyway, there are a few exceptional rules:
(2) When a row has disappeared, then pawns cannot move two squares anymore (moves like e2-e4).
(3) When a column has disappeared, then you cannot castle anymore.
Rule (2) happens rather quickly in most games (row shrinks are frequent early game), but colum shrinks are generally later in the game.
And then we have the most funny rule, that happens occasionally:
(4) When a player promotes an opponents pawn through a shrinking during his move, then the player can decide for the opponent to what the pawn promotes (Knight, bishop, rook or queen).
A player thinking he has won sometimes is surprised by his opponent shrinking and promoting the pawn to a useless knight or bishop. The rule is somewhat logical - if it is your move, and a pawn promotes during your move, then you should be able to decide to what it promotes!
So why is it fun?
Shrink chess is ideal for just fun games, like when you're in a cafe, when you're playing for fun against a stronger/weaker player etc.
Games tend to be too difficult to really calculate ahead, they are quite claustrophobic (boards become smaller but still full), and have a bias towards draws (through stalemates in particular), even a large material advantage can be insufficient to win. The games keep being fun even while losing, not only because of the larger chances for draws (giving you a chance much longer), but also for the strangeness of what happens in the game. It is not very suited for blitz games, as you need time to move all those pieces if you shrink...
In fact, my experience is to play shrink chess just for fun, and not trying to think too far ahead. Or, to do it while you and your opponent have had several beers....
Strategy:
A few strategic hints:
Pawns are worth more, as they are closer to promotion, and "big"pieces like rooks and bishops have less room to maneuver. I tend to give pieces value 2 (2 pawns), but I'm an idiot and don't trust my judgement.
Having said that, material is worth less than in normal games (i.e. position is more important - it is frequent that certain pieces are not involved in play for a long time, or never).
Unless everyone shoves their pawns against the opponent ones, games tend to be quick in the sense that you don't have time to develop pieces, castle, make your position etc.
For the rest, I'll tell you nothing, like how do mates occur at such small boards, you'll figure it out...Ok, one example: white: Ka1, black:Rb2, Kc3:
then black can win in the following way:
1. ... Rb1
2. Ka2
2. ... Rb2 (shrink first row)
and mate on a 3-by-1 board.
(P.S. When writing annotations for a shrink chess game, then shrink "towards the square a1".)
Then, to end, let me give you a problem. White to move, mate in 1
A mate in 1? How hard can it be ! Click the picture for a solution.
Another problem, which is quite hard I guess: white to move and win in 3 moves. It is quite possible to win in other ways, but as far as I saw there's only one solution in 3 moves: